After strong success in producing an effective method of 3D object segmentation by the deformation of m-rep models, we propose to develop generally applicable methodology for segmenting anatomic object structures with a normal topology from medical images and for statistically discriminating normal and diseased states based on the geometry of the extracted objects. We will in particular develop tools required for radiation treatment planning and the diagnosis and scientific study of neurological disorders such as schizophrenia. The methods to be developed involve optimization of Bayesian posteriors learned from training image sets. The posteriors incorporate a prior describing typical geometric structure of an anatomic region and its variation and a likelihood describing the image intensity to geometry relationship. The geometric theory is based on a framework with multiple levels of scale, with the intermediate levels describing objects, figures, and figural sections medially via the m-rep representation, resulting in efficient, effective, and neuroanatomically intuitive analyses. Both of the associated probabilistic structures (prior and likelihood) are hierarchical by scale, based on a Markov random field model. Probability models allowing discrimination will have a similar hierarchical structure, and the discrimination functions will thus indicate with locality and statistical significance the geometric differences that allow discrimination. Our specific aims fall in three areas: Multiscale geometric model development and analysis techniques. We will determine the form and number of levels of multi scale models. We will further develop methods for multi scale model building and for multiscale segmentation. Methods involving probability of multiscale geometry. We will develop means for forming probability distributions describing geometric typicality, and for forming intensity pattern models and their probability distributions. We will find geometric structure representations and their probabilities so as to allow intuitive, effective discriminations between disease states, and we will find means of using training images to indicate geometric homologies. Multi-object and anatomic section segmentation and shape measurement. We will develop methods, in the multi-scale level framework, of extracting multiple objects and of deformation of atlases of full sections of the body into medical image data. We will develop methods of discrimination of geometric patterns that involve multiple objects or full regions of the body.